My partner had this chair all through college, and the seat was getting very worn out. I didn't have the proper socket wrench to disassemble it, so I had to make a cover that fit over it.

I used a scrap of lovely barkcloth I had leftover from another project, and sandwiched it between black cloth I pillaged from a pair of dress pants. The trick was, the seat of the chair has a fold on three sides, that goes in a few inches and then attaches to the base. I sewed a casing and threaded it with elastic to make it behave.